Fundamentals of Fermatean Neutrosophic Soft Set with Application in Decision Making Problem

The classical set theory based on crisp sets is not able to deal with uncertainties whichis a common feature of various real-world problems. This problem is solved using modified forms of sets suchas fuzzy sets, Intuitionistic fuzzy sets, neutrosophic sets, soft sets and hypersoft sets and others along withtheir hybrids. In this paper, a modified hybrid of soft set named Fermatean Neutrosophic Soft set (FrNSS) isestablished. Basic entities of set theory including subsets, null set, universal set along with different operatorsare defined. With respect to these operators, the algebraic structures as monoid, semigroup and semiring aredefined. Also, fermatean neutrosophic soft topological space and the cartesian product of fermatean neutrosophicsoft sets and fermatean neutrosophic soft relation are defined to establish an application of this hybridstructure to decision-making problems.